I am a former Debian user and i appreciated in Debian the way root privileges were exclusive to the SU.It avoided to the lambda user (eg my daughter) to make surprising and sometimes unpleasant administration tasks with its own password.

Can someone please tell me how to replace the user password asked in Mint for any administration task by the real 'Root password' (which, as far as i could notice, doesn't seem to be often asked (exepted at first installation)) ?

I think the default setting for newly added users is no adminstrative privileges.I just created a new user in my Mint VM, through menu->administration->users&groups, logged out, logged in with new user, and could not access admin functions or sudo.